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Expression of type ExprTuple

from the theory of proveit.logic.sets.comprehension

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, S, Variable, n, x
from proveit.core_expr_types import R__x_1_to_n, f__x_1_to_n, x_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([x_1_to_n], Conditional(f__x_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), IndexedVar(S, sub_expr1)), one, n), R__x_1_to_n))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } \left(x_{1} \in S_{1}\right) ,  \left(x_{2} \in S_{2}\right) ,  \ldots ,  \left(x_{n} \in S_{n}\right) ,  R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 12
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 12
4Operationoperator: 6
operands: 7
5Variable
6Literal
7ExprTuple8, 9
8ExprRangelambda_map: 10
start_index: 18
end_index: 19
9Operationoperator: 11
operands: 12
10Lambdaparameter: 25
body: 13
11Variable
12ExprTuple14
13Operationoperator: 15
operands: 16
14ExprRangelambda_map: 17
start_index: 18
end_index: 19
15Literal
16ExprTuple21, 20
17Lambdaparameter: 25
body: 21
18Literal
19Variable
20IndexedVarvariable: 22
index: 25
21IndexedVarvariable: 23
index: 25
22Variable
23Variable
24ExprTuple25
25Variable